cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A272164 a(n) = Product_{k=0..n} (n^2-k)!.

Original entry on oeis.org

1, 1, 288, 53094139822080000, 7114507432973653690572666462301501337370624000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

Comments

The next term has 392 digits.

Crossrefs

Programs

  • Mathematica
    Table[Product[(n^2-k)!, {k, 0, n}], {n, 0, 6}]
    Table[BarnesG[n^2 + 2]/BarnesG[n^2 - n + 1], {n, 0, 6}]

Formula

a(n) = A272163(n) * ((n^2)!)^(n+1) / A272179(n)^n.
a(n) ~ exp(1/24 + n/6 - n^2 - n^3) * n^(1 + n^2 + 2*n^3) * (2*Pi)^((n+1)/2).

A272180 a(n) = Product_{k=0..n} (n^2 + k).

Original entry on oeis.org

0, 2, 120, 11880, 1860480, 427518000, 135970773120, 57274321104000, 30885807297945600, 20759078324729606400, 17018214378110225280000, 16716468557742686853120000, 19383353274717848149493760000, 26198415087179810897268887040000, 40828604361516687201839617904640000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[n^2 + k, {k, 0, n}], {n, 0, 15}]
    Table[n^2*Pochhammer[1 + n^2, n], {n, 0, 15}]

Formula

a(n) ~ exp(1/2) * n^(2*n + 2).

A272241 a(n) = Product_{k=0..n} ((n^2 + k)! / (n^2 - k)!).

Original entry on oeis.org

1, 2, 7200, 474211584000, 1981999450972492922880000, 1401219961854040654113268364083200000000000, 370389015130516478011776928922387124162707119541939129548800000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

Comments

The next term has 95 digits.

Crossrefs

Programs

  • Mathematica
    Table[Product[(n^2+k)!/(n^2-k)!,{k,0,n}],{n,0,7}]
    Table[BarnesG[n^2 - n + 1]*BarnesG[n^2 + n + 2]/(BarnesG[n^2 + 2]*BarnesG[n^2 + 1]), {n, 0, 6}]

Formula

a(n) = A272238(n) / A272164(n).
a(n) ~ exp(5/12) * n^(2*n*(n+1)).

A272237 a(n) = Product_{k=0..n} (n^2+k)^k.

Original entry on oeis.org

2, 180, 2090880, 6044699520000, 7151106328088486400000, 5159620144413185246982598164480000, 3167269298042065159436486399933762922086400000000, 2200712918907364598767850489247066133407004510957047455416320000000
Offset: 1

Views

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[(n^2+k)^k, {k, 0, n}], {n, 1, 10}]
    Table[((n^2+n)!)^(n+1) * BarnesG[n^2 + 1] / BarnesG[n^2 + n + 2], {n, 1, 10}]

Formula

a(n) = ((n^2+n)!)^(n+1) / A272238(n).
a(n) ~ exp(n/3 + 3/8) * n^(n*(n+1)).
Showing 1-4 of 4 results.